Fight Finance

(a) Only (iii) is true.

(b) Only (ii) and (iii) are true.

(c) Only (i), (ii) and (iii) are true.

(d) Either (ii) and (iii) are true, or (iv) is true, or (ii), (iii) and (iv) are true.

(e) Either (i), (ii) and (iii) are true, or (iv) is true, or all are true.

(a) Illiquid small private companies.

(b) Exchange-listed companies operating in stagnant industries with negative growth prospects.

(c) Exchange-listed companies expected to have temporarily high earnings over the next year, but with lower earnings later.

(d) Exchange-listed companies operating in high-risk industries with very high required returns on equity.

(e) Exchange-listed companies whose assets include a very large proportion of cash.

(a) Highly liquid publically listed firms.

(b) Firms in a declining industry with very low or negative earnings growth.

(c) Firms expected to have temporarily low earnings over the next year, but with higher earnings later.

(d) Firms whose returns have a very low level of systematic risk.

(e) Firms whose assets include a very large proportion of cash.

(a) ##-100+ \dfrac{ \dfrac{10}{0.1} \left(1-\dfrac{1}{(1+0.1)^3} \right)}{(1+0.1)^2} +\dfrac{\left(\dfrac{10}{0.1-0.05}\right)}{(1+0.1)^5} ##

(b) ##-100+ \dfrac{10}{(1+0.1)^3} +\dfrac{10}{(1+0.1)^4} +\dfrac{10}{(1+0.1)^5} +\dfrac{\left(\dfrac{10}{0.1-0.05}\right)}{(1+0.1)^5} ##

(c) ##-100+ \dfrac{ \dfrac{10}{0.1} \left(1-\dfrac{1}{(1+0.1)^4} \right)}{(1+0.1)^2} +\dfrac{\left(\dfrac{10.5}{0.1-0.05}\right)}{(1+0.1)^6} ##

(d) ##-100+ \dfrac{10}{(1+0.1)^3} +\dfrac{10}{(1+0.1)^4} +\dfrac{10}{(1+0.1)^5} +\dfrac{10}{(1+0.1)^6} +\dfrac{\left(\dfrac{10.5}{0.1-0.05}\right)}{(1+0.1)^6} ##

(e) ##-100+ \dfrac{ \dfrac{10}{0.1} \left(1-\dfrac{1}{(1+0.1)^3} \right)}{(1+0.1)^3} +\dfrac{\left(\dfrac{10}{0.1-0.05}\right)}{(1+0.1)^5} ##

(a) $758.30

(b) $773.62

(c) $889.87

(d) $944.90

(e) $1,003.33

(a) The returns ##r_\text{t monthly}## are continuously compounded monthly returns and are likely to be normally distributed, so the mean, median and mode of these continuously compounded returns are all equal to 1% per month.

(b) The annualised average continuously compounded return is ##\bar{r}_\text{cc annual}=12×0.01=0.1=12\%\text{ pa}##. The annualised standard deviation is ##\sigma_\text{annual} = \sqrt{12}×0.05=0.173205081=17.32\%\text{ pa}##.

(c) Over the next 10 years the mean, median and mode continuously compounded 10 year returns will all equal ##0.01 \times 12 \times 10 = 120\%##.

(d) Over the next 10 years the expected mean gross discrete 10 year return is ##e^{(0.01 - 0.05^2/2)×12×10} = 2.857651118## and the median gross discrete 10 year return is ##e^{(0.01 + 0.05^2/2)×12×10}=3.857425531##.

(e) If the current price of the CBA shares is $75, then in 10 years they’re expected to have a mean value of ##75×e^{(0.01 + 0.05^2/2)×12×10} = 289.3069148## and a median value of ##75×e^{0.01×12×10}=249.0087692##.

(a) You have a debt asset.

(b) The bank sold you its promise to pay back interest and principal payments.

(c) The bank is exposed to your credit risk, it’s afraid that you’ll default on your debt.

(d) The interest income you’re paid is taxable income for you.

(e) The interest expense that the bank pays is tax-deductible for the bank.

(a) The returns ##r_\text{t monthly}## are continuously compounded monthly returns.

(b) The mean, median and mode of the continuously compounded annual return is expected to equal 0.8% per month.

(c) The annualised average continuously compounded return is ##\bar{r}_\text{cc annual}=12×0.008=0.096=9.6\%\text{ pa}##. The annualised standard deviation is ##\sigma_\text{annual} = \sqrt{12}×0.15=0.519615242 = 52\%\text{ pa}##.

(d) If the current price of the BHP shares is $20, they're expected to have a median value of $52.2339 ##(= 20×e^{0.008×12×10})## in 10 years.

(e) If the current price of the BHP shares is $20, they're expected to have a mean value of $13.5411 ##(= 20×e^{(0.008 - 0.15^2/2)×12×10})## in 10 years.

(a) The number of shares will rise by 2/7 or around 28.5714%.

(b) The share price will fall by 2/7 or around 28.5714%.

(c) If you don't take part in the rights issue and it's non-renounceable, you will lose around $0.6667 per share.

(d) The firm’s market capitalisation of equity will rise by 20/91 or around 21.9780%.

(e) The company will have more cash.

(a) 9.9021%

(b) 9.9431%

(c) 10.4090%

(d) 28.5714%

(e) 100%